Modeling and Analysis of Coupled System for Circular Motion in Machine Tools with XY-Axis Stage

In recent years, the demand for high-speed, high-precision machining has driven the trend toward multi-axis machine tool stages. However, as machine tools become increasingly multi-axis, contour motion errors that cannot be explained by conventional single-axis models have become apparent, necessitating an investigation into their causes. This paper proposes an novel XY-axis interaction model and analyzes contour motion errors arising from circular motion in machine tool stages. The proposed model considers the motion between motor position and stage position, and a non-damped generalized eigenvalue problem for this model can explain contour motion errors caused by axis interaction. Furthermore, the model is designed by applying a least squares method to data measured on a linear scale, eliminating the need for sophisticated measurement equipment. The effectiveness of the proposed model was verified through actual machine testing, suggesting influences from mechanical structure and dynamic characteristics.